Wall and Diaphragm Stresses

Stresses displayed on screen are shown as force per unit area. They are acting on Top/Positive or Bottom/Negative face of shell element.

Table 1. Positive Definition of Stresses: In-Plane (force per unit area)

S11	Normal stress acting on positive and negative face 1 in the direction of axis 1
S22	Normal stress acting on positive and negative face 2 in the direction of axis 2
S12	Shear stress acting on positive and negative face 1 in the direction of axis 2
SMax	Maximum principal normal stress 1
SMin	Minimum principal normal stress 1
SVmax	Maximum principal shear stress 2
Von Mises	Von Mises principal stress 3

1. Principal normal stresses are oriented in such a way that associated shearing stress is zero.
2. Maximum principal shear stress is calculated as follows:
   ${SV}_{max}=Abs\left|\frac{S_{Max}- S_{min}}{2}\right|$
   where

   $S_{Max}$, $S_{min}$

   =

   principal maximum and minimum normal stresses, respectively

3. Von Mises principal stress is calculated as follows:
   $S_{VM}= \sqrt{S_{Max}^2-S_{Max}{S}_{min}+S_{Min}^2}$
   where

   $S_{Max}$, $S_{min}$

   =

   principal maximum and minimum normal stresses, respectively

Table 2. Positive Definition of Stresses: Out-of-Plane-Shear (force per unit area)

S13	Out-of-plane shear stress acting on positive and negative face 1 in the direction of axis 3
S23	Out-of-plane shear stress acting on positive and negative face 2 in the direction of axis 3
SAvgMax	Maximum out-of-plane shear stress1

1. Maximum out-of-plane shear stress is calculated as follows:
   $S_{VM}= \sqrt{S_{13}^2+S_{23}^2}$
   where

   $S_{13}$, $S_{23}$

   =

   out-of-plane stresses in the direction of axis on face 1 and 2, respectively.

Wall and Diaphragm Internal Forces

Internal Forces displayed on screen are shown as force per unit of in-plane length. They are acting at mid-surface of shell element.

Table 3. Positive Definition of Internal Forces: Membrane force (force per unit of in-plane length)

F11	Normal force acting at mid-surface on positive and negative face 1 in the direction of axis 1
F22	Normal force acting at mid-surface on positive and negative face 2 in the direction of axis 2
V12	Shear force at mid-surface acting on positive and negative face 1 in the direction of axis 2
FMax	Maximum principal normal force acting at mid-surface1
FMin	Minimum principal normal force acting at mid-surface1
Von Mises	Von Mises principal force2

1. Principal normal forces are oriented in such a way that associated shearing force is zero.
2. Von Mises principal force is calculated as follows:
   $F_{VM}= \sqrt{F_{Max}^2-F_{Max}{F}_{min}+F_{Min}^2}$
   where

   $F_{Max}$, $F_{min}$

   =

   principal maximum and minimum normal forces, respectively

Table 4. Positive Definition of Internal Forces: Plate moment (moment per unit of in-plane length)

M11	Normal moment acting at mid-surface on positive and negative face 1 about axis 2
M22	Normal moment acting at mid-surface on positive and negative face 2 about axis 1
M12	Twisting moment at mid-surface acting on positive and negative face 1 about axis 1, and on face 2 about axis 2
MMax	Maximum principal moment force acting at mid-surface1
MMin	Minimum principal moment force acting at mid-surface1

1. Principal moments are oriented in such a way that associated twisting moment is zero.

Table 5. Positive Definition of Internal Forces: Transverse shear (shear per unit in-plane length)

V13	Out-of-plane shear acting at mid-surface on positive and negative face 1 about axis 3
V23	Out-of-plane shear acting at mid-surface on positive and negative face 2 about axis 3
VMax	Maximum principal shear1

1. Maximum principal shear is calculated as follows:
   $V_{Max}= \sqrt{V_{13}^2+V_{23}^2}$
   where

   $V_{13}$, $V_{23}$

   =

   out-of-plane shears, respectively

Stress and Internal Force Contours on Wall and Diaphragm

Stresses and internal forces are direction dependent quantities. They are portrayed graphically according to local axes of walls and diaphragms. Local axes of walls and diaphragms are defined as follows (in the following descriptions, right-hand-rule is adapted and, local axes 1, 2 and 3 are perpendicular to each other):

Wall

Local axis 1 and 2 are on plane of wall and local axis 3 is perpendicular to plane of wall. Local axis 2 is always oriented along global axis Z (also note that e2 = e3 x e1). Top (or positive) face of wall is in the direction of positive local axis 3.

Diaphragm with Composite Floor Deck/Slab

If the option Apply Stiffness Modification Factors is selected (see Deck/Slab Property Information dialog in RAM Manager), local axis 1 is in the direction of deck orientation. Local axis 3 is perpendicular to plane of deck. Local axis 2 is constructed from other axes as follows: e2 = e3 x e1.

If the option is not selected, local axes 1, 2 and 3 are in the direction of global axes X, Y and Z, respectively. Top (or positive) face of diaphragm is in the direction of positive local axis 3.

Diaphragm with Noncomposite Floor Deck/Slab

If the option Apply Stiffness Modification Factors is selected (see Deck/Slab Property Information dialog in RAM Manager), local axis 1 is either in the direction of deck orientation (if deck is one-way) or it is defined at user-defined angle measured from global axis (if deck is two-way). Local axis 3 is always perpendicular to plane of deck. Local axis 2 is constructed from other axes as follows: e2 = e3 x e1. If the option is not selected, local axes 1, 2 and 3 are in the direction of global axes X, Y and Z, respectively. Top (or positive) face of diaphragm is in the direction of positive local axis 3.

Diaphragm with Concrete Slab

If the option Stiffness Modifiers is selected (see Deck/Slab Property Information dialog in RAM Manager), local axis 1 is either in the direction of deck orientation (if deck is one-way) or it is defined at user-defined angle measured from global axis (if deck is two-way). Local axis 3 is always perpendicular to plane of deck. Local axis 2 is constructed from other axes as follows: e2 = e3 x e1.

If the option Crack Factors is selected, local axes 1, 2 and 3 are in the direction of global axes X, Y and Z, respectively. Top (or positive) face of diaphragm is in the direction of positive local axis 3.

(a)	(b)

Local axes definitions of (a) wall and (b) diaphragm (global setting shown)